1. Field of the Invention
The present invention relates to a sensor for measurement of the instantaneous rate of mass flow and the cumulative mass flow, in steady or unsteady flows, of single-phase liquids or gases along ducts.
2. Discussion of the Prior Art
The principal criterion for a successful design of a mass flow sensor is that it provides accurate measurements (e.g. xc2x10.5%) of the momentary mass-flow rate in steady and unsteady flows. In certain applications, the criterion that it measure accurately the cumulative mass flow (e.g. xc2x11.0%) over a specified time interval is more appropriate.
For example, in today""s automobile engine, the device used most widely to measure the mass flow rate {dot over (m)} of air into the engine is the mass airflow sensor. The known mass airflow sensor generally comprises a xe2x80x9chot-wirexe2x80x9d sensor housed in the center of a section of a duct as illustrated in FIG. 1 wherein the hot-wire sensor indicates the fluid speed |V| at the duct center.
When the momentary fluid speed is multiplied by the duct cross sectional area A and by the average fluid density xcfx81 (inferred from other measurements of air temperature and pressure), a measure of the mass flow rate m=xcfx81A|V| can be made. In this approach, the implicit assumption that the density across the flow is constant is quite reasonable in engine intake flows. A second implicit assumption, i.e., that the velocity at the duct center is also the velocity over the entire cross sectional area, is not completely valid and so A is replaced with an xe2x80x9ceffectivexe2x80x9darea Aeff determined from a steady flow calibration experiment. More significantly, the hot wire sensor infers fluid speed according to the convective heat transfer from the wire and cannot distinguish the direction of the flow.
Since many ducts flows, and particularly those in intakes to internal combustion engines, are not unidirectional but can momentarily reverse, this existing method may result in incorrect readings of mass flow rate. Consequently, control of the proportions of air and fuel supplied to the engine can be compromised.
Variations on the above described method involve mounting the hot wire sensor within a bypass tube positioned in the duct to damp out unsteadiness in part of the flow, in an effort to remove the directional ambiguity. The presence of the tube obstructs the flow and changes the flow field, necessitating calibration experiments to determine Aeff, though in reality Aeff then becomes a function of time and of the unsteadiness of the particular flow. A schematic of a prior art mass airflow sensor with a bypass duct is shown in FIG. 1.
In addition to the foregoing, venturi and orifice meters are known which measure mass flow rates based on an independent measurement of density and assumptions of steady flow. However, these types of meters are considered to be inadequate in non-steady flows. Turbine meters and moving vane devices also require an independent measure of density and have frequency responses which are too low for automotive intake applications, as well as being intrusive to the flow. Coriolis meters, which have high frequency responses and measure mass flow rate in direct proportion to the Coriolis force, impose large pressure drops on the flow and are most suitable for liquid flow applications.
As such, there is a need in the art for sensors capable of measuring instantaneous rates of mass flow and cumulative mass flow which are non-intrusive.
According to the present invention, the flow rate is determined by measuring a surface force such as the fluid shear stress xcfx84w or the streamwise pressure gradient ∂p/∂x with a sensor of the present invention. While the sensor is preferably enclosed within a duct, the duct itself may be of various cross-sectional shapes, i.e., round, square, eliptical, convoluted, etc. By deducing the flow rate {dot over (m)} or cumulative mass flow mcum from a fluid-mechanics relationship between the mass-flow rate and the measured shear stress, the fluid stress and/or streamwise pressure gradient can be obtained. For fully developed, unsteady, laminar, axisymmetric flow of a Newtonian fluid, these relationships are of the form:                     m        .            ⁢                        ∫          0          t                ⁢                                            (                                                -                                                            ∂                      p                                                              ∂                      x                                                                      ⁢                                  (                                      t                    xe2x80x2                                    )                                            )                        ·                          f              ⁡                              (                                  t                  -                                      t                    xe2x80x2                                                  )                                              ⁢                      ⅆ                          t              xe2x80x2                                            ⁢          xe2x80x83                  m      cum        =                            R          2                v            ⁢                        ∫          0                      t            cum                          ⁢                                            (                                                -                                                            ∂                      p                                                              ∂                      x                                                                      ⁢                                  (                                      t                    xe2x80x2                                    )                                            )                        ·                          g              ⁡                              (                                  t                  -                                      t                    xe2x80x2                                                  )                                              ⁢                      ⅆ                          t              xe2x80x2                                            or            m      .        =          R      ⁢                        ∫          0          t                ⁢                                                            τ                w                            ⁡                              (                                  t                  xe2x80x2                                )                                      ·                          h              ⁡                              (                                  t                  -                                      t                    xe2x80x2                                                  )                                              ⁢                      ⅆ                          t              xe2x80x2                                                      m      cum        =                            R          3                v            ⁢                        ∫          0                      t            cum                          ⁢                                                            τ                w                            ⁡                              (                                  t                  xe2x80x2                                )                                      ·                          j              ⁡                              (                                  t                  -                                      t                    xe2x80x2                                                  )                                              ⁢                      ⅆ                          t              xe2x80x2                                          
where t is time, R is the duct radius, xcexd is the fluid kinematic viscosity, ∂p/∂x is the streamwise pressure gradient, and f g, h, and j are smoothly varying mathematical functions. Processing of shear-stress or pressure gradient measurements with either of these relationships, which involve convolution integrals, are carried out in real-time using an integrated analog-electronics circuit. In specific applications of this kind, where functions f, g, h, and j are known, analog circuits can have higher processing speeds than digital ones. While either shear stress or the pressure gradient could be used as the sensed variable in flows which are fully developed at the sensor location, it is necessary to sense shear stress when the unsteadiness in the flow past the sensor is wave-like.
When compared to the hot-wire mass-airflow sensor used in today""s automobile engine, the present has the advantages that: i) it is wall mounted and therefore non-intrusive to the flow; ii) it can be combined easily with other sensors; iii) it can measure mass-flow rate without requiring an independent measurement of density; and iv) it measures the direction of the flow. Further, when contrasted with orifice meters, the present invention has the advantages of performing accurately in unsteady flow and being able to measure flow direction. When compared with Coriolis meters, the present invention has the advantage that it does not impose a large pressure drop on the flow.
One application for the sensor and methods of the present invention is that automotive engine manufacturers could use the sensor in place of existing mass-airflow sensors in engines as well as for measuring flow rates of mixtures of air, exhaust gases and hydrocarbon vapors in engine intake systems. Still another perceived application for the sensor of the present invention is the measurement of pulmonary flows and other unsteady duct flows in which a surface mounted sensor is preferred.